Asynchronous Whirl Research Articles

Cuttings transport: On the effect of drill pipe rotation and lateral motion on the cuttings bed

Drill pipe rotation is considered a relevant factor for cuttings transport and hole cleaning. However, in the term “rotation” is often used as a moniker for the combination of plain drill pipe rotation around its own axis and more complex lateral motion, as many laboratory setups feature an unconstrained drill string. Lateral motion is generally considered to benefit the transports of cuttings due to increased bed agitation. By means of Computational Fluid Dynamics, we have investigated the effect of synchronous and asynchronous whirling drill string motion on the cuttings bed and cuttings transport for water and a more viscous, shear-thinning fluid using the Two Fluid Model in conjunction with the Kinetic Theory Of Granular Flows and closures from soil mechanics to rheologically describe granular matter. The dynamic mesh capability of ANSYS Fluent R17.2 is exploited to account for the orbital motion of the drill string. In addition, three base cases (negative eccentric, concentric, and positive eccentric) are investigated for comparison. Whirling motion helps tremendously to disperse the solids into the main flow region and hence improves the quality of cuttings transport and hole cleaning, with synchronous whirl by far outperforming asynchronous whirl due to the cumulative tangential and radial velocities. The effect is much more prominent for water than for the more viscous, shear-thinning fluid because the latter already shows a comparatively good cuttings transport performance. Moreover, in case of the more viscous, shear-thinning fluid, the positive eccentric annulus provides an even better cuttings transport capability, if comparison is made on equivalent pressure gradients. Because of the higher viscosity level, the whirling motion reduces the axial throughput, which despite the increased bed agitation results in worse performance compared to the positive eccentric case.

Wave Analysis of Liquid Partially Filling a Rotating Cylinder

Wave motion of a liquid in a rotating, axially symmetric container undergoing a whirl motion is investigated. In the analysis of the present study, gravity is considered to be negligible and the liquid motion is taken as being axially uniform. Assuming that the liquid layer is thin, based on the shallow-water theory, the equations of motion are simplified to a one-dimensional problem along the circumference of the container. The modal coupling equations that include the nonlinear effects of the wave motion are obtained by applying Galerkin's method. Periodical solutions under harmonic whirl motion, which give resonance curves, are determined by applying the harmonic balance method to the modal coupling equations. The wave height and the fluid force acting on the container obtained from the analysis are compared with experimental results reported in previous studies. Good agreement is observed between the results of the present analysis and the experimental results with respect to the wave height profile and the magnitude of the fluid force by which the asynchronous whirl motion of the container is excited.

On the non-linear phenomena due to source loading in rotor—motor systems

The effects of source loading of the drive motor due to rotating material damping induced self-excited asynchronous whirl and unbalance induced synchronous whirl on the overall steady-state behaviour of a rotor—motor system are studied in this article. The formulation is based on finding the existence of a plausible conservative state of the system where the orbital energies are conserved. This method is very simple and, at the same time, it is physically meaningful. The analysis reveals some interesting non-linear phenomena in non-ideal rotor—motor systems. A bond graph model is used to represent the system dynamics. The analytically obtained whirl characteristics are validated through numerical studies.

Asynchronous Dynamic Coefficients of a Three-Lobe Air Bearing

The study of dynamic whirl behavior of air bearings is fundamental for an adequate rotordynamic analysis and future validation of numerical predictions. This work shows the dynamic response of the air film on a three-lobe bearing under asynchronous whirl motion. One-dimensional multifrequency orbits are used to characterize the bearing rotordynamic coefficients. The test rig uses two magnetic bearing actuators to impose any given orbits to the journal. The dynamic forces are measured on the test bearing housing by three load cells. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. The multifrequency excitation is applied at each rotating speed up to 11,000rpm, allowing the asynchronous characterization of the air film. The experimental procedure requires two linearly independent excitation sets. Thus, vertical and horizontal one-dimensional multifrequency orbits are applied as perturbations. Results show the synchronous and asynchronous dynamic coefficients of the air bearing. Asynchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation. Numerical dynamic coefficients are obtained as the effective coefficient values of the bearing when subject to a given orbit. A full characterization of the asynchronous rotordynamics coefficients of the bearing is presented in three-dimensional maps.

Torsional vibration analysis of a multi-body single cylinder internal combustion engine model

This paper presents a detailed multi-body numerical nonlinear dynamic model of a single cylinder internal combustion engine. The model comprises all rigid body inertial members, support bearings, joints, couplers, and connections between the various engine components, as well as means of vibration damping. The detailed model is parameterised, thus enabling virtual prototype testing of various engine designs, as well as allowing the engine designer to carry out a comprehensive noise, vibration, and harshness (NVH) investigation of engine performance. This new approach in engine design reduces the conceptual design-to-development cycle time and removes the need for extensive engine testing, which accounts for a considerable cost in engine design and development process. The model incorporates the simultaneous solution of large displacement dynamics of engine components, infinitesimal vibrations of support bearings, and the trapped air-fuel cylinder transient pressures. The results obtained provide time histories of the dynamic response of all inertial members, such as the piston, the flywheel, and the connecting rod. The torsional vibrations of the crankshaft and both synchronous and asynchronous whirl of journal bearings are also obtained. The simultaneous solution of nonlinear inertial rigid body dynamics, the combustion process, and nonlinear vibrations of the crankshaft main journal bearing supports brings about a new approach in the numerical analysis of complex nonlinear multi-body dynamic problems. Frequency domain analysis of the results shows agreement with generally known experimental spectra. The numerical results also agree with a closed-form analytical solution reported by various authors.

On the stability of a spinning, fluid filled and sectored rotor

The stability of a rigid rotor, spinning at constant angular velocity and having a cylindrical, sectored and fluid filled cavity is analyzed. The cavity is partitioned in n equal sectors by radially extending walls. Each sector is partly filled with the same amount of an inviscid, incompressible fluid. Damping, rotor-unbalance and gravity are considered to be negligible. The analysis predicts several speed ranges of self-excited, asynchronous whirl, the number and size of them depending considerably on the number of sectors and the ratio of polar and axial moments of inertia of the rotor. The theoretical results show good agreement with experimental data.

Analytical and Experimental Investigation of the Coupled Bladed Disk/Shaft Whirl of a Cantilevered Turbofan

The structural dynamics of a rotating flexible blade-rigid disk-flexible cantilevered shaft system is analytically and experimentally investigated. A simple analytical model yields the equations of motion expressed in the rotating frame, which show that the blade one nodal diameter modes dynamically couple to the rigid body whirling motion of the shaft-disk system. The blade modes higher than one nodal diameter are uncoupled from the shaft-disk dynamics. Nondimensionalization of the coupled equations of motion yield the criteria for the propensity and magnitude of the interaction between the bladed disk and shaft-disk modes. The analytical model was then correlated with the results of a structural dynamic experiment performed on the MIT Aeroelastic Rotor, a fan similar in design to a modern high bypass ratio shroudless turbofan. A special whirl excitation apparatus was used to excite both forward and backward asynchronous whirl, in order to determine the natural frequencies of the system. The agreement between the predicted and experimental natural frequencies is good and indicates the possibility of significant interaction of the one nodal diameter blade modes with the shaft-disk modes.

Asynchronous Instability of a Rotating Centrifuge Partially Filled With Fluid

An experimental investigation of the asynchronous whirl motion of a partially filled rotating centrifuge on an elastic support system has been performed. Whirl runout amplitudes are measured and the data are used to deduce the stability boundaries of the asynchronous whirl. The effects of various parameters on the stability boundaries are studied systematically. These parameters are the fill ratio, mass ratio, Reynolds number, and the damping of the elastic support system. The experimental results are compared with theoretical predictions based on a linear analysis. Free surface shapes are compared with results of nonlinear analysis.

Asynchronous whirl in a rotating cylinder partially filled with liquid

Experimental and analytical results are presented for the self-excited oscillations that occur in a partially filled centrifuge when centrifugal forces interact with shallow-water waves. Periodic and aperiodic modulations of the basic whirl phenomena are both observed and calculated. The surface waves are found to be hydraulic jumps, undular bores or solitary waves.

Whirl Dynamics of a Rotor Partially Filled With Liquid

A spinning rotor, mounted on an elastic shaft and containing a symmetrically located cylindrical chamber partially filled with liquid, is assumed to undergo a small whirling motion. In the analysis, rotor unbalance, gravity, and gyroscopic terms are considered negligible, and the liquid motion is taken as being axially uniform. The added liquid produces a lowering of the usual synchronous critical speed. In addition, waves in the liquid layer couple with rotor whirl motion to produce a range of self-excited asynchronous whirl speeds above the critical, similar to those observed for nonsymmetrical solid rotors. Experiments completely corroborate the analytical results.

The Influence of Trapped Fluids on High Speed Rotor Vibration

Fluids are often introduced accidentally and trapped inside of high speed rotors. This has given concern as to the possible deleterious effects of such trapped fluids on the system’s vibration characteristics. Trapped fluids will induce asynchronous vibratory motion of high speed rotors at supercritical rotational speeds. This tendency is examined in analytic detail. Assuming that the circumferential velocity of the trapped fluid varies linearly with radius, the generalized shape of the fluid film is derived. Integrating the fluid pressure on the cavity walls gives the net fluid forces and permits computation of whirl frequency and whirl amplitude as functions of rotative speed. Generalized plots are given of the film geometry, of the rotative speed at which asynchronous whirl starts, and of the induced whirl speed. General response curves are also given, showing whirl amplitude as a function of rotative speed. The detailed results indicate that whirl occurs at a rotative speed approximately double the induced whirl frequency (as happens with many rotor whirl mechanisms). Higher values of the system parameter g result in somewhat lower whirl onset speeds. The whirl velocity is approximately equal to the rotor critical speed, or slightly lower for large masses of trapped fluid. Rotor whirl amplitude increases sharply with rotative speed above onset speed until a limiting condition where the fluid film (and analytic solution) break down, at a rotative speed about 6 percent above onset speed. Trapped fluids will also influence the normal synchronous vibrations induced by rotor unbalance. Analyses of a simple model of synchronous, solid body rotation are made which give exact solutions for the condition of a fully welted cavity periphery, and give approximate solutions for a partially welted periphery. It is concluded that the trapped fluid generally reduces the critical frequency, reduces critical amplitude, and reduces high speed (supercritical) amplitude. The effect is quite small with a partially welted circumference, but is surprisingly large in the case where the periphery of the cavity stays fully welted at maximum vibration amplitude. In this case, the rotor acts as if the cavity were entirely full of fluid, even though actual trapped fluid may fill only a small fraction of the cavity volume! Significant reductions in critical frequencies and amplitude are thereby observed. In the case of systems that are partially welted in going through their resonance peak, a “rightward leaning” resonance peak is observed which results in jump phenomena and hysteresis in amplitude on accelerating and decelerating through the peak.